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We observe that a large class of well behaved stationary and axisymmetric black hole solutions in general relativity and in the Einstein-Maxwell theory can be classified according to the properties of their background. Indeed all these…
To what extent are all astrophysical, dark, compact objects both black holes (BHs) and described by the Kerr geometry? We embark on the exercise of defying the universality of this remarkable idea, often called the "Kerr hypothesis". After…
We prove uniqueness of the Kerr black holes within the connected, non-degenerate, analytic class of regular vacuum black holes.
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds.…
In general relativity, all vacuum black holes are described by the Kerr solution. Beyond general relativity, there is a prevailing expectation that deviations from the Kerr solution increase with the horizon curvature. We challenge this…
The spacetime singularities in classical general relativity are inevitable, which are also predicated by the celebrated singularity theorems. However, it is general belief that singularities do not exist in the nature and they are the…
The spacetime around astrophysical black holes is thought to be described by the Kerr solution. However, even within general relativity, there is not yet a proof that the final product of the complete collapse of an uncharged body can only…
Many discussion about the black hole conundrums, such as singularity and information loss, suggested that there must be some essential irreconcilable conflict between quantum theory and classical gravity theory, which cannot be solved with…
We propose a novel black hole model in which singular and regular black holes are combined as a whole and more precisely singular and regular black holes are regarded as different states of parameter evolution. We refer to them as singular…
We revisit the classical thermodynamic stability of the standard black hole solutions by implementing the intrinsic necessary and sufficient conditions for stable global and local thermodynamic equilibrium. The criteria for such equilibria…
Black hole entropy of the Kerr-like family of spacetimes is introduced as the canonical charge on the horizon. Treating these spacetimes in the framework of Poincar\'e gauge theory either as Riemannian solutions or as solutions with…
Recently our understanding of black holes in D-spacetime dimensions, as solutions of the Einstein equation, has advanced greatly. Besides the well established spherical black hole we have now explicitly found other species of topologies of…
Black-hole uniqueness, i.e., the statement that all stationary vacuum black holes in the universe are described by the Kerr solution, is expected to break in theories beyond General Relativity. This breaking can take a particularly strong…
Between 1972 and 1975, Jacob Bekenstein proposed that black holes possess entropy proportional to their horizon area, and Stephen Hawking derived this relationship from semiclassical quantum field theory in curved spacetime, predicting…
A new solution of four-dimensional vacuum General Relativity is presented. It describes the near horizon region of the extreme (maximally spinning) binary black hole system with two identical extreme Kerr black holes held in equilibrium by…
The idea that black holes (BHs) result in highly excited states representing both the "hydrogen atom" and the "quasi-thermal emission" in quantum gravity is today an intuitive but general conviction. In this paper it will be shown that such…
It is now widely accepted that the universe as we understand it is accelerating in expansion and fits the de Sitter model rather well. As such, a realistic assumption of black holes must place them on a de Sitter background and not…
Ever since its discovery by Roy Kerr in 1963, the geometry around rotating, electrostatically-neutral black holes, otherwise known as Kerr black holes, has significantly contributed to theoretical developments in the fields of general…
We review our recent work on linear stability for scalar perturbations of Kerr spacetimes, that is to say, boundedness and decay properties for solutions of the scalar wave equation \Box_g{\psi} = 0 on Kerr exterior backgrounds. We begin…
It is well known that the concept of black hole has been considered very fascinating by scientists even before the introduction of Einstein's general relativity. They should be the final result of an irreversible gravitational collapse of…